{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Data Analysis, 3rd ed\n",
    "##  Chapter 4, demo 1\n",
    "\n",
    "Normal approximaton for Bioassay model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import optimize, stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "# add utilities directory to path\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)\n",
    "# apply custom background plotting style\n",
    "plt.style.use(plot_tools.custom_styles['gray_background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Bioassay data, (BDA3 page 86)\n",
    "x = np.array([-0.86, -0.30, -0.05, 0.73])\n",
    "n = np.array([5, 5, 5, 5])\n",
    "y = np.array([0, 1, 3, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# compute the posterior density in grid\n",
    "#  - usually should be computed in logarithms!\n",
    "#  - with alternative prior, check that range and spacing of A and B\n",
    "#    are sensible\n",
    "ngrid = 100\n",
    "A = np.linspace(-4, 8, ngrid)\n",
    "B = np.linspace(-10, 40, ngrid)\n",
    "ilogit_abx = 1 / (np.exp(-(A[:,None] + B[:,None,None] * x)) + 1)\n",
    "p = np.prod(ilogit_abx**y * (1 - ilogit_abx)**(n - y), axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following demonstrates an alternative \"bad\" way of calcuting the posterior density p in a for loop. The vectorised statement above is numerically more efficient. In this small example however, it would not matter that much.\n",
    "\n",
    "    p = np.empty((len(B),len(A))) # allocate space\n",
    "    for i in range(len(A)):\n",
    "        for j in range(len(B)):\n",
    "            ilogit_abx_ij = (1 / (np.exp(-(A[i] + B[j] * x)) + 1))\n",
    "            p[j,i] = np.prod(ilogit_abx_ij**y * ilogit_abx_ij**(n - y))\n",
    "\n",
    "N.B. the vectorised expression can be made even more efficient, e.g. by optimising memory usage with in-place statements, but it would result in a less readable code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# sample from the grid\n",
    "nsamp = 1000\n",
    "samp_indices = np.unravel_index(\n",
    "    np.random.choice(p.size, size=nsamp, p=p.ravel()/np.sum(p)),\n",
    "    p.shape\n",
    ")\n",
    "samp_A = A[samp_indices[1]]\n",
    "samp_B = B[samp_indices[0]]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "samp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "samp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50\n",
    "samp_ld50 = - samp_A / samp_B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the mode by minimising negative log posterior. Compute gradients and Hessian analytically, and use Newton's method for optimisation. You may use optimisation routines below for checking your results. See help for scipy.optimize.minimize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define the optimised function\n",
    "def bioassayfun(w):\n",
    "    a = w[0]\n",
    "    b = w[1]\n",
    "    et = np.exp(a + b * x)\n",
    "    z = et / (1 + et)\n",
    "    e = - np.sum(y * np.log(z) + (n - y) * np.log(1 - z))\n",
    "    return e\n",
    "# initial guess\n",
    "w0 = np.array([0.0, 0.0])\n",
    "# optimise\n",
    "optim_res = optimize.minimize(bioassayfun, w0)\n",
    "# extract desired results\n",
    "w = optim_res['x']\n",
    "S = optim_res['hess_inv']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# compute the normal approximation density in grid\n",
    "# this is just for the illustration\n",
    "\n",
    "# Construct a grid array of shape (ngrid, ngrid, 2) from A and B. Although\n",
    "# Numpy's concatenation functions do not support broadcasting, a clever trick\n",
    "# can be applied to overcome this without unnecessary memory copies\n",
    "# (see Numpy's documentation for strides for more information):\n",
    "A_broadcasted = np.lib.stride_tricks.as_strided(\n",
    "    A, shape=(ngrid,ngrid), strides=(0, A.strides[0]))\n",
    "B_broadcasted = np.lib.stride_tricks.as_strided(\n",
    "    B, shape=(ngrid,ngrid), strides=(B.strides[0], 0))\n",
    "grid = np.dstack((A_broadcasted, B_broadcasted))\n",
    "p_norm = stats.multivariate_normal.pdf(x=grid, mean=w, cov=S)\n",
    "\n",
    "# draw samples from the distribution\n",
    "samp_norm = stats.multivariate_normal.rvs(mean=w, cov=S, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ULWzpSMP3zYMKHyGEEEJIzKHC1w9aqNkrH7awXZq9hU0r2/Xo2hRdUzIerDhLE9FWK7aq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\n4au1so1a8eqUTK2f20m5dxO7O883rvn0IKRU4q4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9u1NvItxsDBiEjMQo4DW+hPQTW2Hr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MriXNvqzwy47z28GDSN1u4wFYVBNq6sJGQYcQez9NZvUtXSck/OBibX5etv7aelJ4oG1HeGefLG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\nkiRlzsAnSZKUuf8PfsLU9bmiSasAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7010ca9198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create figure\n",
    "fig, axes = plt.subplots(3, 2, figsize=(9, 10))\n",
    "\n",
    "# plot the posterior density\n",
    "ax = axes[0, 0]\n",
    "ax.imshow(\n",
    "    p,\n",
    "    origin='lower',\n",
    "    aspect='auto',\n",
    "    extent=(A[0], A[-1], B[0], B[-1])\n",
    ")\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.grid('off')\n",
    "\n",
    "# plot the samples\n",
    "ax = axes[1, 0]\n",
    "ax.scatter(samp_A, samp_B, 5)\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.text(0, -7, 'p(beta>0)={:.2f}'.format(np.mean(samp_B>0)))\n",
    "\n",
    "# plot the histogram of LD50\n",
    "ax = axes[2, 0]\n",
    "ax.hist(samp_ld50, np.linspace(-0.8, 0.8, 31))\n",
    "ax.set_xlim([-0.8, 0.8])\n",
    "ax.set_xlabel(r'LD50 = -$\\alpha/\\beta$')\n",
    "ax.set_yticks(())\n",
    "ax.set_xticks(np.linspace(-0.8, 0.8, 5))\n",
    "\n",
    "# plot the posterior density for normal approx.\n",
    "ax = axes[0, 1]\n",
    "ax.imshow(\n",
    "    p_norm,\n",
    "    origin='lower',\n",
    "    aspect='auto',\n",
    "    extent=(A[0], A[-1], B[0], B[-1])\n",
    ")\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.grid('off')\n",
    "\n",
    "# plot the samples from the normal approx.\n",
    "ax = axes[1, 1]\n",
    "ax.scatter(samp_norm[:,0], samp_norm[:,1], 5)\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "\n",
    "# Normal approximation does not take into account that the posterior\n",
    "# is not symmetric and that there is very low density for negative\n",
    "# beta values. Based on the samples from the normal approximation\n",
    "# it is estimated that there is about 4% probability that beta is negative!\n",
    "ax.text(0, -7, 'p(beta>0)={:.2f}'.format(np.mean(samp_norm[:,1]>0)))\n",
    "\n",
    "# Plot the histogram of LD50\n",
    "ax = axes[2, 1]\n",
    "# Since we have strong prior belief that beta should not be negative we can\n",
    "# improve our normal approximation by conditioning on beta>0.\n",
    "bpi = samp_norm[:,1] > 0\n",
    "samp_ld50_norm = - samp_norm[bpi,0] / samp_norm[bpi,1]\n",
    "ax.hist(samp_ld50_norm, np.linspace(-0.8, 0.8, 31))\n",
    "ax.set_xlim([-0.8, 0.8])\n",
    "ax.set_xlabel(r'LD50 = -$\\alpha/\\beta$')\n",
    "ax.set_yticks(())\n",
    "ax.set_xticks(np.linspace(-0.8, 0.8, 5))\n",
    "\n",
    "fig.tight_layout()"
   ]
  }
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